Improved Fourier Modal Method Analyzing 2-D Ultrathin Periodic Structures Without Solving Eigenvalues

Intensive computation for solving eigenvalues of large eigenmatrix restricted the development of Fourier modal method (FMM) in analyzing periodic structures, especially 2-D ultrathin periodic structures. To alleviate the problem of intensive computation in the traditional FMM algorithm when analyzing 2-D ultrathin periodic structures, an efficient FMM algorithm without solving eigenvalues is proposed in this letter. Based on the first-order Taylor Expansion, the exponential term matrix in the traditional algorithm can be replaced by two simple diagonal matrices, which avoids the large dimensional matrix inversion process, and the newly formed execution equation is only related to the eigenmatrix. Two numerical examples show that the results of the traditional FMM algorithm, improved FMM algorithm and CST simulation, are highly consistent. Compared with the traditional algorithm, the improved algorithm can greatly alleviate the computing-intensive problems, and the improved algorithm can significantly reduce the CPU time by more than 90% and reduce computation memory by about 70%.